Finite-size effects in the spherical model of ferromagnetism: Antiperiodic boundary conditions

Explicit expressions are derived for the free energy, the specific heat, and the magnetic susceptibility of a spherical model of spins on a d-dimensional hypercubical lattice, of size $L_1$×$L_2$×...×$L_d$, under antiperiodic boundary conditions. The relevant scaling functions that govern the critical behavior of the system are obtained and, with the use of the asymptotic properties of these functions, various predictions of the Privman-Fisher hypothesis [Phys. Rev. B 30, 322 (1984)] on the hyperuniversality of finite systems are verified. Approach towards standard critical behavior, both for T<$T_c$(∞) and T>$T_c$(∞), is examined. In the former case, the approach generally takes place through a power law; only in some special situations does one obtain an exponential law instead. In the latter case, the approach is generally exponential, except for the susceptibility of the system which (somewhat surprisingly) displays a finite-size effect dominantly determined by the surface-to-volume ratio of the lattice.